few_shots: Example:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Standard options: 
A. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
B. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
C. Fluently multiply multi-digit whole numbers using the standard algorithm.


Thought: This set of problems involves multi-digit whole numbers because the numbers in each problem are four and two digit integers, and the mathematical calculations involved in both problems focus on multiplication. The first problem explicitly asks the student to solve its subproblems using the standard algorithm.
Answer: C

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_000674

5
options: Analyze and solve pairs of simultaneous linear equations.

Solve linear equations in one variable.
problem_activity: Optional activity
In this activity, students solve a variety of systems of equations, some involving fractions, some involving substitution, and some involving inspection. This gives students a chance to practice using the methods they have learned in this section for solving systems of equations to solidify that learning. Some of the systems listed are ones students could have used in an earlier activity in this lesson, to describe the situations there. In the discussion, students compare the systems here to the ones they wrote in that activity and interpret the answer in that context.
Launch
Keep students in groups of 2. Allow students 5–7 minutes of partner work time followed by a whole-class discussion.
Representation: Internalize Comprehension
. Activate or supply background knowledge. Allow students to use calculators to ensure inclusive participation in the activity.
Supports accessibility for: Memory; Conceptual processing
Student Facing
Here are a lot of systems of equations:
\(\begin{cases} y=\text-2x+6 \\ y=x-3 \end{cases}\)
\(\begin{cases} y=5x-4 \\ y=4x+12 \end{cases}\)
\(\begin{cases} y=\frac23x-4 \\ y=\text-\frac43x+9 \end{cases}\)
\(\begin{cases} 4y + 7x = 6 \\ 4y+7x = \text-5 \end{cases}\)
\(\begin{cases} y=x - 6\\ x=6 + y \end{cases}\)
\(\begin{cases} y=0.24x\\ y=0.18x+0.9 \end{cases}\)
\(\begin{cases} y=4.5x+15 \\ y=5x+12.5 \end{cases}\)
\(\begin{cases} y=3x \\ x+y=52 \end{cases}\)
Without solving, identify 3 systems that you think would be the least difficult for you to solve and 3 systems you think would be the most difficult. Be prepared to explain your reasoning.
Choose 4 systems to solve. At least one should be from your "least difficult" list and one should be from your "most difficult" list.
Student Response
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Activity Synthesis
There are two key takeaways from this discussion. The first is to reinforce that some systems can be solved by reasoning whether its possible for a solution to one equation to also be a solution to another. The second takeaway is that there are some systems that students will only be able to solve after learning techniques in future grades.
For each problem, ask students to indicate if they identified the system as least or most difficult. Record the responses for all to see.
Bring students' attention to this system:
\(\begin{cases} 4y + 7x = 6 \\ 4y+7x = \text-5 \end{cases}\)
Ask students what the two equations in the system have in common to each other and to think about whether a solution to the first equation could also be a solution to the second. One can reason there is no solution because
\(4y+7x\)
cannot be equal to both 6 and -5.
Ask students to return to the earlier activity and see if they can find any of those systems in these problems. (Lin's family ride is the sixth system. Noah's kayaking trip is the seventh system. Diego's baking is the eighth system.) After students notice the connection, invite students who chose those systems to solve to interpret the numerical solutions in the contexts from the earlier activity.
Students may be tempted to develop the false impression that all systems where both equations are given as linear combinations can be solved by inspection. Conclude the discussion by displaying this system that students defined in the last activity about sugar and flour:
\(\begin{cases} 0.8x+0.5y = 9 \\ x+y = 15 \end{cases}\)
Tell students that this system has one solution and they will learn more sophisticated techniques for solving systems of equations like this in future grades.
Speaking, Listening, Conversing: MLR8 Discussion Supports.
Before the whole-class discussion, use this routine to give students an opportunity to discuss their reasons for labeling systems of equations as “least difficult” or “most difficult.” Provide the following sentence frame: “_____ is the least/most difficult to solve because _____.” Encourage listeners to press for detail by asking questions such as “What would make that problem easier to solve?”; “What do your least/most difficult problems have in common?” This will help students make connections between the structures of given systems of equations, and possible strategies they can use to solve them.
Design Principle(s): Cultivate conversation; Maximize meta-awareness


correct_option_index: 0